INSTRUMENTAL MEASUREMENT OF ANGLES AND TIME.
GRADUATED CIRCLES.—Astronomy is essentially a science of precision, and
the progress of our knowledge has to a large extent been dependent upon
the increasing power of accurately measuring angles and time.
Let us see, first of all, how to measure angles.
A circle is divided into 360 degrees, each degree again into 60 minutes,
and each minute into 60 seconds of arc; and yet, a second of arc is not
a small enough quantity for many astronomical purposes. Now, unless a
very large circle be employed, it is mechanically impossible to even
mark the minutes of arc directly upon it, and if a very large circle
were constructed, the distortion of its shape produced by its own weight
would be sufficient to mar its accuracy.
What is actually done then is to get a circle of convenient size, and to
graduate it, as well as the highest mechanical skill is capable of, into
such parts as may leave distinct and equal spaces between the separate
divisions. A competent instrument maker would, for instance, put 4,320
divisions on the _limb_ of a circle 16 inches in diameter, two
consecutive divisions thus being 5′ apart. For work of the highest
precision it is necessary to strictly investigate the errors of the
divisions and to correct for them in all observations.
For the further subdivision of these graduations, verniers or reading
microscopes are introduced.
THE VERNIER.—A graduated circle being attached to an instrument, what
one has to do is to take a _reading_ with reference to some fixed mark.
If the fixed mark is seen to fall precisely on one of the divisions of
the circle when observed with a magnifying-glass, the reading can be
written down exactly. If there be no such coincidence, some means are
required for accurately reckoning the fraction of a division. One method
in general use on small instruments, and where extreme precision is
unnecessary, is to employ a subsidiary scale which is called a
_Vernier_, in honour of the Frenchman who invented it. This can be
applied indifferently to a scale of degrees and parts of degrees on a
graduated circle, or to a straight scale. With the aid of this device it
becomes possible to measure angles with no greater probable error than a
few seconds of arc.
[Illustration:
FIG. 47.
]
THE READING MICROSCOPE.—If a greater degree of accuracy than 10″ be
required, the vernier is superseded by a _reading microscope_. This is a
compound microscope (Fig. 48) by which the scale can be observed, and at
the focus of its eye-piece is a pair of spider threads which can be
moved by a fine screw S. Looking into such a microscope, one sees a
magnified picture of a very small part of the scale running through the
field of view, as in Fig. 47. Running across the field, in the same
direction as the marks on the scale, are the spider threads _a b_, which
can be given a right and left movement by means of the screw. At the top
of the field is the part called the “comb,” having its edge cut with
saw-like teeth; like the threads, this is at the focus of the eye-piece.
The scale is divided so that the smallest part is 5′, and in that case
the teeth of the comb are arranged so that five of them equal a scale
division. The reading microscope is a fixture, and the circle is brought
into the position in which its reading is required by moving the
instrument with which it is connected. The zero of the microscope is a
point at the middle of the comb, and one has to determine what part of
the scale corresponds with it. In order to do this, the threads or
“wires” are moved until the next division lies between them, and the
amount which the screw has been turned from the position of zero is read
off on the graduated head of the screw. The dimensions of the parts, and
the magnifying power of the microscope, are adjusted so that the screw
must be turned five times to carry the wires through a space equal to a
division on the scale. One division, therefore, will move the wires
through 1′, and as the screw head is divided into 60 parts, a movement
of ¹⁄₆₀th of a revolution will shift the wires through a second of arc.
Even fractions of a second can be thus measured.
[Illustration:
FIG. 48.—_The Reading Microscope._
]
The introduction of this method of measuring minute angles is due to
Ramsden, who first applied it at the end of the last century. The
microscopes themselves are used for measuring fractional parts of the
graduations of the circles, and usually four to six of them are applied
to different parts of the same circle. In this way, errors arising from
flexure of the circle, fluctuations of temperature, want of exact
circularity, etc., are eliminated, so that finally, after taking every
conceivable precaution, the astronomer can measure angles with the
accuracy which is absolutely necessary in many branches of research.
ASTRONOMICAL CLOCKS.—Means for the exact estimation of time are of no
less importance in an observatory than arrangements for the accurate
measurement of angles. Astronomical clocks are constructed with extreme
care, but in principle they do not differ from ordinary time-keepers. As
sidereal time is of the greatest use in an observatory, the hour hand
only makes one revolution a day, and the face is provided with a seconds
hand, which is plainly visible. The pendulum is of such a length that it
performs its swing in a second. One of the most important improvements
in clocks was the introduction of the “compensation” principle, whereby
the equivalent length of a pendulum remains constant in spite of
fluctuations of temperature. The mercurial pendulum which one very
frequently sees in a watchmaker’s establishment has a glass or steel
cylinder near the bottom partly filled with mercury; as the rod
lengthens by increased temperature, the centre of gravity is raised by a
corresponding amount, on account of the upward expansion of the mercury,
and the rate of swing remains constant when the quantity of mercury is
properly adjusted. The chief defect of this plan is that the mercury and
the steel rod do not respond equally well to a change of temperature.
In the most approved clocks the pendulum rod is a compound one,
consisting of rods, or concentric tubes, of zinc and steel. The pendulum
bob is hung on a steel rod suspended from the top of a zinc tube, which
in turn is fixed at the bottom end to a larger tube of steel; a rod
attached directly to the latter is suspended by a flat spring in the
usual manner. By this arrangement the unequal expansions or contractions
of the different parts due to changes of temperature neutralise each
other, so that a constant rate is the result. The tubes are pierced with
numerous holes so that the inner and outer ones acquire the same
temperature almost at the same time.
The rate of a clock is disturbed slightly by changes in the pressure of
the atmosphere. When the air is densest there is a greater resistance to
the swinging of the pendulum, and the clock will go more slowly.
Although this only amounts to a small fraction of a second a day, it
must necessarily be taken into account in such an establishment as that
at Greenwich, to which all the country looks for the precise control of
time-keepers. In the standard clock at Greenwich a magnet is raised or
lowered by the changing height of a barometer, and its varying
attraction upon a certain piece of iron attached to the pendulum
compensates for the differences produced by change of pressure.
Pendulum clocks are obviously unsuitable for use at sea, so that
_chronometers_ are usually employed on ships. These are like large
watches, very carefully constructed, with “compensation” balance wheels,
and can generally be relied upon as good time-keepers.
After all precautions, however, no astronomer would put his faith in any
clock for any length of time, as the best of them is liable to change
its rate rather irregularly. The “error” of the clock is therefore very
frequently determined by the observation of certain standard stars with
the transit instrument. The stars can be relied upon to come to the
meridian at the proper time, and any apparent departure from this time
must be set down to the account of the clock.
THE CHRONOGRAPH.—A good clock, however, is not the only requirement of
an observatory. It is necessary further to be able to record very
precisely the moment at which an observation is made. If the clock be in
the immediate vicinity of the observer, the time can be noted by
counting the beats of the pendulum, and a practised observer will, by
this “eye and ear” method, record times to the nearest tenth of a
second. Mere estimation, however, is not very reliable, so that a
mechanical method, which also permits greater subdivision of the second,
is very generally adopted. The instrument is called a _chronograph_,
and, although constructed in various forms, its function is to record on
a sheet or strip of paper the regular beats of the clock, as well as the
signals made by the observer. In one form of the instrument the
recording sheet is fixed on a cylindrical drum which is made to revolve
once a minute by a small clock. Beneath the drum is a pair of prickers
worked by the armatures of electromagnets. One of these magnets is in
connection with the clock, and a simple arrangement sends an electric
current through it every second, with the result that the seconds are
marked by small punctures on the paper. As the cylinder revolves, the
marker travels slowly lengthwise, so that the clock record runs spirally
from one end to the other. To facilitate the identification of the
punctures, one is omitted at the end of every minute. When an
observation is made, the observer presses a button, and a current is
sent through the second magnet, with the result that a puncture is made
alongside those made by the clock. In this way the exact moment at which
an observation is made can be easily registered, and read off at any
convenient time.
At Greenwich a room is set apart for a number of chronographs, each in
communication with an instrument in the various observatories.